Non-Iterative Numerical Solutions of Boundary-Value Problems,
NAVAL ORDNANCE LAB WHITE OAK MD
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Use is made of the exact anlaytical solution of a related difference-equation problem, which can be found under a large variety of circumstances. This analytical solution is used to set up and check a stepping-ahead process, during which the numerical solution of the boundary-value problem is obtained as though the governing differential equation were hyperbolic instead of elliptic. This paper discusses application of the technique when the governing equation is linear this equation may be non-homogeneous, of any order, and with any number of independent variables moreover, the region over which the equation is solved can be geometrically irregular. Furthermore, since the technique in effect solves a high-order system of simultaneous linear equations of simple but nontrivial structure, it constitutes a new approach to matrix inversion.
- Theoretical Mathematics